The inclined position of a vehicle is described, as a rule, by roll angle φ. It is known, from the related art, that roll rate W of the vehicle can initially be measured with the aid of a roll rate sensor, and that roll angle φ can be determined by subsequently integrating the roll rate. However, the value determined in this manner only represents an amount Δφ, by which the roll angle has changed during the integration phase. On the other hand, initial value φ0 at the beginning of the integration (offset) is not known. Thus, calculated roll angle φ includes an offset error. In addition, since changes in the roll angle are added to the current value, all of the occurring errors add up. Consequently, the roll rate is not stable over the long term. Therefore, a useful determination of roll angle φ according to common methods requires a further method for determining the roll angle, e.g., a model-based approach using the yaw rate and the longitudinal vehicle speed, in order to consequently compensate for the offset error.
Normally, both a roll rate sensor and a yaw rate sensor are used for determining roll angle φ. Roll angle φ is then determined, on one hand, according to the above-mentioned integration methods, and calculated, on the other hand, in a model-based manner, in view of the yaw rate. However, the two methods for determining roll angle φ have certain limitations to their accuracy. Therefore, the roll angle φ ultimately used by a vehicle system is ascertained by combining the two methods. This method for determining roll angle φ requires two rotation rate sensors and is, therefore, relatively expensive.